Mathematics
In the figure (2) given below, PQRS is a parallelogram formed by drawing lines parallel to the diagonals of a quadrilateral ABCD through its corners. Prove that area of || gm PQRS = 2 × area of quad. ABCD.
Theorems on Area
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Answer
From figure,
Area of ∆ACD = Area of || gm ACRS [As both are on same base AC and between the same parallel lines AC and SR]
⇒ Area of || gm ACRS = 2 Area of ∆ACD …….(i)
Similarly,
Area of ∆ABC = Area of || gm ∆APQC [As both are on same base AC and between the same parallel lines AC and PQ]
⇒ Area of || gm APQC = 2 Area of ∆ABC …….(ii)
Adding (i) and (ii),
⇒ Area of || gm ACRS + Area of || gm APQC = 2 Area of ∆ACD + 2 Area of ∆ABC
⇒ Area of || gm PQRS = 2[Area of ∆ACD + Area of ∆ ABC]
⇒ Area of || gm PQRS = 2(Area of quad. ABCD)
Hence, proved that area of || gm PQRS = 2 x area of quad. ABCD.
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